ABSTRACT
The Fourier transform of a discrete signal, which is referred to as the discrete-time Fourier transform (DTFT) is a special case of the z-transform in as much as the Fourier transform of a continuous signal is a special case of the Laplace transform. In the present discrete-time context we write for simplicity Fourier transform to mean the DTFT. We will, moreover, see in this chapter that the discrete Fourier transform (DFT) is a sampled version of the DTFT, in as much as the Fourier series is a sampled version of the Fourier transform of a continuous signal. The chapter ends with a simplified presentation of the fast Fourier transform (FFT), an efficient algorithm for evaluating the DFT.
